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Probability and Math Finance Seminar

Christian Gromoll, Department of Mathematics, University of Virginia

Fluid limits for shortest remaining processing time queues


In an SRPT queue, the server always works on the job with the shortest remaining processing time, that is, the job that can be completed first. There has been recent renewed interest in the SRPT policy due to its relevance to scheduling in web servers. This talk will describe a fluid model for GI/GI/1/SRPT queues. A key feature of this model is an explicit description of the evolution of the "left edge," the largest service time of any job that has entered service. Understanding the left edge dynamics gives an explicit formula for the fluid analogue of response time, the time a job of given size must wait for service. This result holds under quite general distributional assumptions. The talk will also outline a limit theorem establishing the fluid model as a first order approximation of the stochastic model. This is joint work with D. Down and A. Puha.

MONDAY, September 8, 2008
Time: 5:00 P.M.
Location: WeH 6423